Multi-parameter Quantum Groups and Quantum Shuffles, (I)
Abstract
In this article, we study the multi-parameter quantum groups defined by generators and relations associated with symmetrizable generalized Cartan matrices, together with their representations in the category O. This presentation will be convenient for our later discussions. We present two explicit descriptions here: as a Hopf 2-cocycle deformation, and as the multi-parameter quantum shuffle realization of the positive part.
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